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BLADE ELEMENT MOMEMTUM CODE FOR HORIZONTAL AXIS WIND AND MARINE CURRENT

TURBINES BEMMCT. PACK I.

Copyright 2010. Alexander Ladino, MSc.

[email protected]

Description and Pack Content.

BEMMCT is a MATLAB Toolbox designed to perform computations in

conceptual and general design phase of horizontal axis wind turbines

(HAWCT) and Horizontal Axis Marine Current Turbines (HAMCT) . The code is

based on the classical Blade Element Momentum Method BEM. The code is

highly vectorized in order to improve speed computing.

The pack is composed by:

1.

Script bemmain1.m which the packs main program.

2.

Function bemcore.m: BEM core solver called from bemmain.m3.

Script postprocoeffblade.m and postprocoeff.m: scripts for

postprocessing stage.

4.

Specialized functions: Used in computation stage and they are called

by bemcore.m during BEM calculation.

5.

preprocessing scripts: Scripts and templates used in order to

generate the main parameters required for BEM computation.

About the guide.

This guideline explain the main characteristics of BEMMCT pack, the main

routines and general steps and requirement to perform BEM computations of

a horizontal axis wind and marine current turbine.This document is divided three parts:

1.How to perform a BEM analysis.

2.Function and script documentation.

How to perform a BEM analysis

The following paragraphs contain information step to step in order to

perform a Blade Element Momentum analysis. These steps are divided in 3

general stages: Geometry Definition, Profiles Definition, Simulation

Parameters and Postprocesing

a.Geometry definition (script geomdef.m).

The following data are required for blade definition (all of that are

defined respect to dimensionless span r/R):

Dimensionless span r/R: rR.

Dimensionless chord c/R: cR

Local blade pitch or local twist angle (deg): pitch

For blades composed by NACA profiles, it is necessary to define thickness

distribution: thickness

Dimensionless chord at blade root: crhub.

Dimensionless chord at blade tip: crtip.

Dimensionless hub radius: rhubnd.

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Defining these parameters and running the script a filename.mat file will

be saved containing the information about the blade geometry definition.

b.

Profiles Definition: Aero / Hydrodynamic data (template

naca638xxre300k.m)

In order to perform BEM computations, it is necessary to define the liftand drag coefficients for the profiles used in the blade geometry.

This version only supports two kinds of profile definition in blade

geometry:

a.

NACA profiles of the same series varying only thickness:

Ex: naca638xxre300k.m

b.

Only one profile of any designation (Ex: NACA, Selig, Eppler e.t.c).

Ex: naca4412re300k.m

In general, the functions must load cl and cd data

Ex: x63812300kpol.mat)1

and it is necessary that lift and drag data covera wide range of angles of attack (minimum -90 to 90deg). Also, the data

must be in increasing order for aoa, for example:

aoa Cl

-90 0

-85 0.01

-70 0.005

Data for airfoils can be obtained from the following links:

http://www.ae.illinois.edu/m-selig/ads/coord_database.htmlhttp://isoar.ca/~andrewm/rc/airfoils/

http://www.worldofkrauss.com/

On the other hand, airfoils can be computed using XFOIL or Javafoil,

However be careful with the data since the range of confidence is only

limited to pre stall regime, and it is necessary to use some models to

extrapolate aerodynamic data for high angles of attack.

Finally, the exit variables from the function are cl and cd coefficients

evaluated at each local angle of attack at each radial position along the

blade.

c.Simulation Parameters (Script bemmain1.m)

The following lines are the Input section of bemmain1.m where turbine

properties are defined.

1. %% Inputs

2. % Results filename to save

3. filesave = 'bahajmctres.mat';

1The mat file containing information of cl and cd, must have the following variable

names: For lift coefficient: clinfo. For drag coefficient: cdinfo. Both with

dim(numangles,2) where numangles are the number of data, the column 1 is the angle of

attack and column 2 is the coefficient.

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4. % ----- TURBINE PROPERTIES -----

5. % Turbine Geometry *.mat file

6. bladedata = 'bahajmct.mat';

7. % airfoil data function

8. mct.foilfcn = @naca638xxre300k;

9. % blade composed by different AIRFOILS. 1: Yes; No:010. nacacomp = 1;

11. % number of blades

12. nblades = 3;

The lines are explained below:

Line3: Write between the quotes the file name used to save the simulation

results. DO NOT FORGET THE MATLAB RESULTS FILE EXTENSION .mat

Line6: Write between the quotes the file name where turbine geometry is

defined (from geometry definition section a). DO NOT FORGET THE MATLAB

RESULTS FILE EXTENSION .mat

Line 8: Write after @ the function filename where lift and drag data are

defined (from profiles definition).

Line 10: Flag. Write 1 if the blade is composed by different naca

profiles or naca profiles with different thickness.

Line 12: write the number of turbine blades (usually 3)

The following lines are the simulation conditions of bemmain1.m where

turbine properties are defined.

1: % ---- SIMULATION CONDITIONS ----

2: % TIP SPEED RATIO REGIME

3: TSR = [2:0.5:10];

4: % hub twist angles

5: settippitch = [0 5 10 12];

Line 3: Tip Speed Ration regime. Write the range of TSR and the increment

to be simulated [TSRmin:Increment:TSRmax];

Line5: settippitch. Write the pitch angle rotation of the blade. It is

possible to simulate the turbine for different pitch rotations. Ex:

settippitch = [ang1 ang2 ang3 angn].

The following lines are the solver parameters and conditions of

bemmain1.m where turbine properties are defined.

1: % ---- SOLVER CONDITIONS ----

2: % calc hub loss? 1: YES, 0: NO

3: hubloss = 1;

4: % calc tip loss? 1: YES, 0: NO

5: tiploss = 1;

6: % maximun number of iterations7: maxit = 200;

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8: % number of elements

9: numele = 30;

10: % Termination criteria

11: tole = 1e-3;

12: % solucion weighting factor successive substitutions)

13: relaxfactor = 0.2;

Line3: Write 1 if Hub losses will be computed or 0 if not (Default 1).

Line5: Write 1 if Tip losses will be computed or 0 if not (Default 1).

Line7: Write the maximum number of iterations (Default 200).

Line9: Write the number of blade elements in which the blade will be

divided. (Default 30).

Line11: Write the convergence tolerance. (Default 1e-3 min 1e-5).

Line13: Write the weighting factor for successive substitutions. (1

implies that computed solution is the new solution. [0

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In order to run the script, press the key f5. The postprocessing presents

MATLAB graphs which can be manipulated in standard way (save as *.fig,

save as image, e.t.c).

The following image is and example of postprocesing of a Bahajs Marine

Current Turbine.

-

Variables along blade span: Script postprocoeffblade.m

1: % ENTER FILENAME

2: filename = ['bahajmctres.mat'];

3: % set the tsr to be ploted (-1 to plot all tsr available in results

file)

4: tsrplot = [4 5 6 7];

5: % set the pitchplot (settippitch) to be plotted (999 to plot all pitch

angle available in results file)

6: pitchplot = [0 5 10 12];

Line2: Write between the quotes the results filename (file written by

bemmain1.m). DO NOT FORGET THE MATLAB RESULTS FILE EXTENSION .mat

Line4: tsrplot: Write the tsr desired to be plotted. To plot all tsr

available in the results file write -1. Note: The tsr to be plotted must

be the exactly the same those were resolved. Interpolation between

results is not available in this version.

Line6: pitchplot: Write the pitch angle desired to be ploted. To plot all

pitch angles available in the results file, write 999. Note: The pitch to

be ploted must be the exactly the same that were resolved. Interpolation

between results is not available in this version.

In order to run the script, press the key f5. The postprocessing presents

MATLAB graphs which can be manipulated in standard way (save as *.fig,

save as image, e.t.c).

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Routines, scripts and functions of BEMHAWT&MCT.

The following functions are the program functions used in BEMHAWT&MCT.

Function afactor.m

Computes the axial induction factor based on Classical Blade ElementTheory and Glauert Corrections. Moriarty & Hansen. Aerodyn Theory manual.

National Renewable Energy Laboratory. www.nrel.gov. AND Bahaj. The

Prediction of Hydrodynamic Performance of Marine Current Turbines.

Renewable Energy 33 (2008) 1085 - 1096.

Inputs:

dct: local thrust coefficient dim(1,numele) where numele is the

number of blade elements.

cnorm: normal coefficients at each blade element dim(1,numele) where

numele is the number of blade elements.

floss: Total loss factor dim(1,numele) where numele is the number ofblade elements.

phi: angle between the incident velocity and rotor plane at each

blade element dim(1,numele).

lsigma: local solidity at each blade element: dim(1,numele) where


Outputs:

afactor: local axial induction factor dim(1,numele)

Function aini.m

computes the initial axial induction factor. based on Moriarty & Hansen.

Aerodyn Theory manual. National Renewable Energy Laboratory. www.nrel.gov.

Inputs:

beta: angles between rotor plane and blade element chords

dim(1,numele) where numele is the number of blade elements.

ltsr: local tip speed ratio at blade element dim(1,numele)

lsigma: local solidity dim(1,numele).

Outputs:

afini: local initial axial induction factor dim(1,numele)

Function apfactor.m

Computes the tangential induction factor based onClassical Blade Element Theory. Bahaj. The Prediction of Hydrodynamic

Performance of Marine Current Turbines. Renewable Energy 33 (2008) 1085 -

1096.

Inputs:

ctan: tangential coefficients at each blade element dim(1,numele)

where numele is the number of blade elements.

floss: Total loss factor dim(1,numele) where numele is the number of

blade elements.



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lsigma: local solidity at each blade element: dim(1,numele) where


Outputs:

apfactor: local tangential induction factor dim(1,numele)

Function bemcore.mCore solver for Blade Element Momentum Calculations. Computes the

principal parameters for a wind and marine current turbine.

Inputs:

- mct: structure of turbine parameters

mct.rpos: dimensionless radial positions along the blade. It

must be strictly hubroot < rpos < 1. Where root is the

dimensionless hub radius. dim(1,numele) where numele are the

number of elements per blade to be computed.

mct.cr: dimensionless chord c/R. where c is the real chord

lenght and R is the turbine radius.mct.tc: thickness/chord ratio (For NACA airfoils only)

dim(1,numele)

mct.pitch: array of blade element angles. dim(1,n)

mct.lsigma: local solidity mct.cr.*nblades./(2.*pi.*mct.rpos)

dim(1,numele)

- parms: structure of solution parameters

parms.tol: termination criteria

parms.maxit: maximum number of iterations

parms.hubloss: 0. do not compute hub loss factor

1. compute hub loss factor

parms.tiploss: 0. do not compute tip loss factor1. compute tip loss factor

parms.relaxfactor: relaxation factor solution update

0 < parms.relaxfactor

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results.apfactor: local operation tangential induction factor

dim(numele,numTSR)

results.dct: local thrust coefficient dim(numTSR,1) where

numTSR is the number of tip speed ratio regime.

results.dcp: local power coefficient dim(numTSR,1) where numTSR

is the number of tip speed ratio regime.results.ctt: total thrust coefficient dim(numTSR,1) where

numTSR is the number of tip speed ratio regime.

results.cpt: total power coefficient dim(numTSR,1) where numTSR

is the number of tip speed ratio regime.

Function coeffnt.m

Computes the normal and tangential coefficients in the turbine.

Inputs:

cl: lift coefficients at each blade element dim(1,numele) where


cd: drag coefficients at each blade element dim(1,numele) wherenumele is the number of blade elements.



Outputs:

cnorm: normal coefficients at each blade element dim(1,numele) where




Function ctcoef.m

Computes the local thrust coefficient based on classical Blade ElementMomentum Theory. Bahaj. The Prediction of Hydrodynamic Performance of

Marine Current Turbines. Renewable Energy 33 (2008) 1085 - 1096.

Inputs:

afactor: Axial induction factor dim(1,numele) where numele is the


cnorm: normal coefficient dim(1,numele) where numele is the number

of blade elements.



lsigma: local solidity at each blade element: dim(1,numele) wherenumele is the number of blade elements.

Outputs:

dct: local thrust coefficient dim(1,numele) where numele is the


Function cxcoef.m

Computes the local coefficients based on classical Blade Element Momentum

Theory. Bahaj. The Prediction of Hydrodynamic Performance of Marine

Current Turbines. Renewable Energy

33 (2008) 1085 - 1096.

Inputs:

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afactor: Axial induction factor dim(1,numele) where numele is the


cnorm: normal coefficient dim(1,numele) where numele is the number

of blade elements.


where numele is the number of blade elements.phi: angle between the incident velocity and rotor plane at each


TSRj: Global Tip Speed Ratio

mct: structure array containing turbine information.

mct.lsigma: local solidity at each blade element: dim(1,numele)


mct.rpos: dimensionless position of each blade element


mct.deltar: blade element radial size.

mct.numblades: number of turbine blades.

Outputs:dct: local thrust coefficient dim(1,numele) where numele is the


dcp: local power coefficient dim(1,numele) where numele is the


cpt: total power coefficient dim(1,numTSR) where numTSR is the

number of tip speed ratio regime.

ctt: total thrust coefficient dim(1,numTSR) where numTSR is the

number of tip speed ratio regime.

Function geomturbineinterp.m

Computes the geometrical parameters of a turbine blade using cubicinterpolation

Inputs:

- parmsori: structure. parmsori defines the blade parameters in

dimensionless form.

parmsori.cR: dimensionless chord along the blade c/R where c is

the local chord length and R is the blade Radius

parmsori.rR: dimensionless position along the blade r/R.

parmsori.pitch: local blade pitch angle.

- rpos: dimensionless positions along the blade where blade

data are required for BEM computations.

Outputs:

- cRI: dimensionless chord along the blade for local

dimensionless positions rpos.

- pitchI: blade pitch angle along the blade for local

dimensionless positions rpos.

Outputs:

- cRI: c/R relation for each blade element station dim(1,numele)


- pitchI: pitch distribution for each blade element station


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- thicknessI: thickness distribution for each blade element

station dim(1,numele) where numele is the number of blade

elements.

Function hubloss.m

Computes the Hub Loss factor. Based on Moriarty & Hansen. Aerodyn Theorymanual. National Renewable Energy Laboratory. www.nrel.gov.

Inputs:



rhubnd: dimensionless hub position

rpos: dimensionless position of each blade element dim(1,numele)


numblades: number of turbine blades.

Outputs:

fhub: hub loss factor dim(1,numele) where numele is the number ofblade elements.

Function naca638xxre300k.m

Computes interpolated values for lift and drag coefficients of naca 638xx

airfoil series of Bahaj's Marine Current Turbines.

Inputs:

parms: structure array containing

parms.tc: airfoil thickness distribution dim(1,numele) where numele

is the number of blade elements.

only used if the blade is composed by a series of airfoil ofdifferent thickness

parms.aoa: local angle of attack dim(1,numele) where numele is the


Outputs:

Cl: lift coefficient of each blade element dim(1,numele) where


Cd: drag coefficient of each blade element dim(1,numele) where


Note: This function can be used as a template in order to construct other

data base of airfoils for turbines blades.

Function phiang.m

Computes the angle phi between the incident velocity and rotor plane at

each blade element dim(1,numele) where numele is the number of blade

elements.

Inputs:

ltsr: local tip speed ratio dim(1,numele)

afactor: axial induction factor dim(1,numele)

apfactor: tangential induction factor dim(1,numele)

Function spaceresults.m

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Allocates space for results array for a BEM simulation.

Inputs:

- mct: structure of turbine parameters

mct.rpos: dimensionless radial positions along the blade. It

must be strictly hubroot < rpos < 1. Where root is thedimensionless hub radius. dim(1,numele) where numele are the

number of elements per blade to be computed.

mct.cr: dimensionless chord c/R. where c is the real chord

lenght and R is the turbines radius.

mct.tc: thickness/chord ratio (For NACA airfoils only).

dim(1,numele)

mct.pitch: array of blade element angles. dim(1,n)

mct.lsigma: local solidity mct.cr.*nblades./(2.*pi.*mct.rpos).

dim(1,numele)

- ext: structure of operation conditions:

ext.settippitch: pitch angle offset from the original bladegeometry. (scalar).

ext.TSR: array of increasing Tip Speed Ratio Regimes

dim(1,numTSR). Where m is the number of TSR's to be computed.

Outputs:

- results: structure array. composed by:

*results.phi: local inplane rotor - flow angle.

dim(size(rpos),size(TSR),size(settippitch))

*results.aoa local angle of attack.


*results.cl local lift coefficient.

dim(size(rpos),size(TSR),size(settippitch))*results.cd local drag coefficient.


*results.ctan local tangential coefficient.


*results.cnorm local normal coefficient.


*results.afactor local axial induction factor.


*results.apfactor local tangential induction factor


*results.dct local thrust coeffient.


*results.dcp local power coefficient.


*results.ctt total thrust coeffienct

dim(size(TSR),size(settippitch));

*results.cpt total power coeffienct

dim(size(TSR),size(settippitch));

Function tiploss.m

Computes the Prandtl Tip Loss factor. Based on Moriarty Hansen. Aerodyn

Theory manual. National Renewable Energy Laboratory. www.nrel.gov.

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Inputs:



rpos: dimensionless position of each blade element dim(1,numele)


numblades: number of turbine blades.Outputs:

ftip: tip loss factor dim(1,numele) where numele is the number of

blade elements.

Function writeresults.m

Save variables in results structure (See function spaceresults.m)

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